Both "disappointed in" and "disappointed at" are idiomatic in American English. In general in American English, people tend to use "disappointed in" with reference to a specific person or group of people.
The difference between "in", "by", and "with" in this context actually depends on the nature or type of disappointment you feel: "Disappointed with" implies that the cause of the disappointment was something basic about the nature or attributes of the thing: I was disappointed with my new toaster. It really didn't toast the bread as well as I hoped. The "with" form is usually used with ...
grammar - Is it disappointed with, in, or by? - English Language ...
Both Don't be discouraged and Don't be disappointed are perfectly natural things to say, and in many contexts they'll effectively mean the same thing - speaker is advising someone to look on the bright side (to find good things in a bad situation). As OP has discovered, the dictionary definitions are somewhat different, but they're obviously closely related. A "defeatist" reaction to finding ...
If one thinks "disappointed" must be accompanied by at least some tinge of dejection, the lawyer's phrase "agreeably disappointed" will seem oxymoronic -- or the word "agreeably" itself will have to be twisted to mean "not too disagreeably" as you have done with "not too torn up about it".
Usage of "I am agreeably disappointed in" - English Language Learners ...
I'd like to know which preposition to use in the following: We were disappointed in/at the fact that no one is interested in our products.
Of the list you provide, "in" is the most idiomatic, but there's also "disappointed by ", "disappointed with ", and "disappointed at " a person or persons. You can, apparently, be "disappointed of " some expected result, which can include the actions of some person. However, to me this sounds formal and somewhat archaic, and I would never use use it. As far as I know, "disappointed from " is ...